Abstract

As a measure of dynamical structure, short term fluctuations of coherencebetween 0.3 and 100 Hz in the electroencephalogram (EEG) of humans were studied from recordings made by chronic subdural macroelectrodes 5-10 mm apart, on temporal, frontal and parietal lobes, and from intracranial probes deep in the temporal lobe, including the hippocampus, during sleep, alert and seizure states. The time series of coherence between adjacent sites calculated every second or less often varies widely in stability over time; sometimes it is stable for half a minute or more. Within two minute samples, coherence commonly fluctuates by a factor up to 2 or 3, in all bands, within the time scale of seconds to tens of seconds. The power spectrum of the time series of these fluctuations is broad, extending to 0.02 Hz or slower, and is weighted toward the slower frequencies; little power is faster than 0.5 Hz. Some records show conspicuous swings with a preferred duration of 5-15 s, either irregularly or quasi-rhythmically with a broad peak around 0.1 Hz. Periodicity is not statistically significant in most records. We have not found a consistent difference between lobes of the brain, subdural and depth electrodes or sleeping and waking states, in our sampling. Seizures generally raise the mean coherence in all frequencies and may reduce the fluctuations by a ceiling effect. The coherence time series of different bands is positively correlated (0.45 overall); significant non-independence extends for at least two octaves. Coherence fluctuations are quite local; the time series of adjacent electrodes is correlated with that of the nearest neighbor pairs (10 mm) to a coefficient averaging ca. 0.4, falling to ca. 0.2 for neighbors-but-one (20 mm) and to < 0.1 for neighbors-but-two (30 mm). The evidence indicates fine structure in time and space, a dynamic and local determination of this measure of cooperativity. Widely separated frequencies tending to fluctuate together exclude independent oscillators as the general or usual basis of the EEG, although a few rhythms are well known under special conditions. Broadband events may be the more usual generators. Loci only a few mm apart can fluctuate widely in seconds, either in parallel or independently. Scalp EEG coherence cannot be predicted from subdural or deep recordings, or vice versa and intracortical microelectrodes show still greater coherence fluctuation in space and time 1. Widely used computations of chaos and dimensionality, made upon data from scalp or even subdural or depth electrodes, even when reproducible in successive samples, cannot be considered representative of the brain or the given structure or brain state but only of the scale or view (receptive field) of the electrodes used. Relevant to the evolution of more complex brains, which is an outstanding fact of animal evolution, we believe measures of cooperativity are likely to be among the dynamic features by which major evolutionary grades of brains differ. In spite of a large literature on the electroencephalogram, we have an extremely limited picture of the structure of activity in the brain on the scales of millimeters and seconds. In spite of a prevailing view that the principal generators of the compound field potentials in the brain are microscopic, cellular or subcellular and chiefly membrane potentials, our extant data base is mainly scalp recordings on humans, usually 40 mm apart, each conservatively estimated to take the vector sum of activity in ca. 15 million cells, assuming a volume 1.5 mm deep x 10 x 10 mm tangentially at 50,000 neurons per cubic millimeter and an equal number of glia. In spite of an extensive knowledge of cellular interaction by synaptic mechanisms, our quantitative understanding of the amount of interaction by this route versus electrotonic or chemical field effects is almost nil. Under such circumstances, we consider quite vulnerable such concepts as synchronization, resonance, rhythmicity and independence of frequency components of the EEG - each an inference, but seldom measured. The present report is one of a series aiming at some insight into the fine structure in space and time of the dynamical signs provided in the compound field potentials, as recorded directly on or in the brain 1, 2, 3, 4, 5, 6, 7, 8, 9. The main goal is to test the hypothesis that one measure of cooperativity at each frequency, namely coherence, varies in time on the scale of seconds or fractions of a second, with evidence of more than stochastic structure and that the fluctuation is different for closely spaced loci. We will show in addition that a wide range of frequency components of the EEG tend to covary in coherence, contrary to the usual assumption of independent oscillators.